bg physiological signal processing 04 signal sampling and reconstruction2020mk 7993

Nguyễn Công PhươngPHYSIOLOGICAL SIGNAL PROCESSING Signal Sampling and Reconstruction... Signal Sampling and Reconstruction VI... Signal Sampling and Reconstruction • Periodic Sampling of

Nguyễn Công Phương

PHYSIOLOGICAL SIGNAL PROCESSING

Signal Sampling and Reconstruction

I Introduction

II Introduction to Electrophysiology

III Signals and Systems

IV Fourier Analysis

V Signal Sampling and Reconstruction

VI The z-Transform

Signal Sampling and

Reconstruction

• Periodic Sampling of Continuous – Time

Signals

• Frequency Analysis of Periodic Sampling

• Reconstruction of Continuous – Time Signals from Samples

• Discrete Processing of Continuous – Time

Signals

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Signal Sampling and

Reconstruction

Sensor Analog Pre-processing

ADC DSP DAC Analog Post-processing

Analog input

Analog output

Periodic Sampling

of Continuous – Time Signals

Ideal analog – digital converter

Signal Sampling and

Reconstruction

• Periodic Sampling of Continuous – Time

Signals

• Frequency Analysis of Periodic Sampling

• Reconstruction of Continuous – Time Signals from Samples

• Discrete Processing of Continuous – Time

Signals

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Frequency Analysis of Periodic

Frequency Analysis of Periodic

frequency Nyquist frequency

X jΩ = Ω > Ω

Then x c (t) can be uniquely determined by its samples x[n] = x c (nT), where

n = 0, ±1, ±2, …, if the sampling frequency Ωs satisfies the condition

Signal Sampling and

Reconstruction

• Periodic Sampling of Continuous – Time

Signals

• Frequency Analysis of Periodic Sampling

• Reconstruction of Continuous – Time

Signals from Samples

• Discrete Processing of Continuous – Time

Signals

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Reconstruction of Continuous –Time Signals from Samples (1)

2 (n − )T

Reconstruction of Continuous –Time Signals from Samples (2)

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Reconstruction of Continuous –Time Signals from Samples (3)

F s = 1/T

[ ]

Reconstruction of Continuous –

Time Signals from Samples (4)

sin[ ( ) / ] ( ) [ ]

x

1 [ ]

x g t −T

0 [ ] ( )r

x g t

Discrete – time Fourier Transform Pairs

/ /

Reconstruction of Continuous –Time Signals from Samples (6)

Ideal digital – analog converter

F s = 1/T

[ ]

Ideal analog – digital converter

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Reconstruction of Continuous –Time Signals from Samples (7)

F

No aliasing

0

2 0

X j π F = G j π F X e π

Reconstruction of Continuous –Time Signals from Samples (8)

F

Aliasing

2 ( )

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Reconstruction of Continuous –Time Signals from Samples (9)

Reconstruction of Continuous –Time Signals from Samples (10)

Signal Sampling and

Reconstruction

• Periodic Sampling of Continuous – Time

Signals

• Frequency Analysis of Periodic Sampling

• Reconstruction of Continuous – Time Signals from Samples

• Discrete Processing of Continuous – Time

Signals

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Discrete – Time Processing of Continuous – Time Signals (1)

Discrete – Time Processing of Continuous – Time Signals (3)

Discrete – Time Processing of Continuous – Time Signals (5)

Y j

T

π π

Discrete – Time Processing of Continuous – Time Signals (7)

1 1

n

T

n n

2 2